AQA A Level Physics

Topic Questions

7.8 Magnetic Fields

1a3 marks

Figure 1 shows a current carrying conductor at an angle θ to an external B field. 

Figure 1

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F=BIL sin θ

is used to calculate the force acting on the current carrying conductor at different angles, θ, to the B field. 

State what the symbols B, I and L

1b1 mark

State the angle, θ, between the conductor and the B field which would result in the largest force being exerted on the conductor.

1c1 mark

State the angle, θ, between the conductor and the B field which would result in there being no force exerted on the conductor from the B field.

1d2 marks

The conductor in Figure 1 has a length of 1.2 m and has a current of 0.85 A flowing through it. The conductor is placed at 30o to the B field, which has a magnetic flux density of 70 mT. 

Calculate the force acting on the conductor.

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2a3 marks

When the force, the magnetic field and the current are all mutually perpendicular to each other, the directions of each can be interpreted by Fleming’s left–hand rule, as shown in Figure 1.

Figure 1

7-8-s-q--q2a-easy-aqa-a-level-physics'

State what is represented by the direction of: 

(i)

The thumb

(ii)

The first finger

(iii)

     The second finger

2b1 mark

Figure 2 shows a magnetic B field. 

Figure 2

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State whether the magnetic field is acting into or out of the page.

2c2 marks

A circuit is built with a section of wire, between the points A and B, running perpendicular to a magnetic field, as shown in Figure 3

Figure 3

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When the switch is closed, state the direction of: 

(i)         The current through wire AB

(ii)        The force acting on wire AB.

2d2 marks

State two ways of increasing the size of the force acting on the current carrying conductor.

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3a2 marks

State the definition for magnetic flux density.

3b1 mark

State the unit for magnetic flux density.

3c4 marks

A wire of length 15 cm has a mass of 30 g and a 2.0 A of current flowing through it. When it is paced inside a uniform magnetic field, as shown in Figure 1, the wire ‘floats’ in equilibrium in the magnetic field. 

Figure 1

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(i)

Calculate the weight of the wire

(ii)

Hence determine the size of the force produced by the magnetic field acting on the wire when it is carrying current

3d3 marks

Calculate the magnetic flux density required to keep the wire ‘floating’ in equilibrium.

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4a4 marks

The equation used to calculate the force acting on a moving charged particle is: 

         F = BQv 

State what each symbol in the above equation represents.

4b2 marks

A beam of electrons is fired into a uniform magnetic field of flux density 0.5 T, as shown in Figure 1

Figure 1

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An electron enters the magnetic field at point A

Draw an arrow, labelled F, from point A to show the direction of the force acting on the electron.

4c2 marks

The electron is travelling at a speed of 4.8 × 107 m s–1. 

Calculate the force on the electron when it enters the magnetic field and is travelling perpendicular to it. 

Remember that the magnetic field has a magnetic flux density 0.5 T

4d4 marks

On Figure 1, continue the path of the electron beam:

(i)         Through the magnetic field 

(ii)        After it has emerged from the magnetic field

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5a3 marks

When a moving charge enters a magnetic field the magnetic field produces a force on the charge, which can be calculated using 

         F = Bqv 

where B is the magnetic flux density, q is the charge and v is its velocity. 

The magnetic force provides the centripetal force which causes the charge to move in a circular orbit. The equation to calculate the centripetal force acting on an object is: 

         Ffraction numerator m v squared over denominator r end fraction 

where m is the mass of the object, v is the speed of the object and r is the radius of the circular orbit. 

Using the equations given above, show that the radius of the circular orbit of the charged object inside the magnetic field can be given as: 

         r =fraction numerator m v over denominator B q end fraction

5b3 marks

State three ways of increasing the radius of the circular orbit.

5c2 marks

An electron is travelling at right angles to a uniform magnetic field which has a magnetic flux density of 5.6 mT. The speed of the electron is 3.0 × 106 m s–1. 

Use the following information to calculate the radius of the circular orbit of the electron: 

            Mass of an electron = 9.11 × 10–31 kg

            Charge of an electron = 1.60 × 10–19 C

5d1 mark

Name the particle accelerator which accelerates charged particles along a spiral path.

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1a3 marks

A mass spectrometer is an instrument used to analyse the atoms present in a sample of gas. The atoms are ionised in order to produce positive ions and then passed through a velocity selector, as shown in Figure 1.

The velocity selector consists of electric and magnetic fields acting at right angles to each other. The magnetic field acts into the page. The electric field is produced by a pair of parallel plates of separation d with a high potential difference, V, across them.

Figure 1

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Discuss how the velocity of an ion affects the path it takes through the velocity selector.

1b2 marks

Calculate the velocity of each ion passing straight through the selector when the magnetic field strength is 260 mT, the potential difference across the plates is 1200 V and the plate separation is 2 cm.

1c4 marks

A mixture of ionised lithium isotopes, of mass 6 u and 7 u leave the velocity selector with a velocity of 4.8 × 104 m s-1.The ions enter a uniform magnetic field which exerts a force on them causing them to strike the detector. The upper edge of the detector is 40 mm from the point at which the charged ions enter the field, as shown in Figure 2.

Figure 2

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Calculate the maximum magnetic field strength that can be applied in order for both ions to be detected.

Each ion has a charge of +1.6 × 10-19 C.

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2a3 marks

A wire is held in tension between two fixed points, X and Y. A short section of the wire is positioned between the pole pieces of a permanent magnet, which applies a uniform horizontal magnetic field at right angles to the wire, as shown in Figure 1. 

Figure 1

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Explain why the wire will vibrate vertically when an alternating electric current is passed through the wire.

2b3 marks

The length of XY is 0.40 m. When the wire is vibrating, transverse waves are propagated along the wire at a speed of 32 m s–1.

Explain why the wire is set into large amplitude vibration in the first harmonic mode when the frequency of the a.c supply is 40 Hz.

2c2 marks

A magnetic field of flux density 240 mT is produced by the permanent magnet and acts over a 60 mm length of the wire.

Calculate the maximum force on the wire when there is an alternating current of rms value 2.8 A through it.

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3a4 marks

An electron passes between two adjacent chambers.  Each chamber contains a separate, uniform magnetic field. The magnetic field strength in the first chamber is 1.5 mT and the magnetic field strength of the second chamber is half that of the first chamber. The electron enters the first chamber perpendicular to the top surface and leaves the second chamber perpendicular to the bottom surface. The horizontal displacement of the electron after passing through the chambers is 90 mm, as shown in Figure 1. 

Figure 1

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Calculate the velocity at which the electrons enter the first chamber.

3b5 marks

A cyclotron is a particle accelerator which consists of two D-shaped electrodes, called ‘dees’, enclosed in an evacuated chamber, as shown in Figure 2. A high frequency, alternating square-wave potential difference, of amplitude begin mathsize 16px style V subscript 0 end style, is applied between the gap of the dees.  When a charged particle crosses the gap between the dees the polarity reverses causing the particle to be accelerated by the potential difference between the dees.  

Figure 2

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Under a magnetic field of 0.500 T and a square-wave potential difference of amplitude 340 V, particles of mass 6.64 × 10-27 kg and charge +3.20 × 10-19 C leave the cyclotron at Y where the radius is 0.750 m. 

Calculate the number of revolutions that the charged particle undergoes before exiting the cyclotron.

3c3 marks

Determine the frequency needed for the charged particle to be accelerated each time it crosses from one dee to the other.

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4a3 marks

Figure 1 shows an electron moving through a magnetic field. 

Figure 1

7-8-s-q--q4a-hard-aqa-a-level-physics

 

The magnetic field has a flux density of 0.38 T. The electron travels at a speed of 1.2 × 107 m s–1. 

Calculate, as a percentage, the reduction in magnetic force acting on the electron when it moves at an angle of 30° through the magnetic field compared to moving perpendicular to the magnetic field.

4b2 marks

Two electrons, X and Y, travel in a uniform magnetic field. X has kinetic energy, K E subscript X, and Y has kinetic energy,K E subscript Y . 

Calculate the ratio begin mathsize 16px style fraction numerator K E subscript X over denominator K E subscript Y end fraction end style if X travels at 30° and Y travels perpendicular to the field.

4c2 marks

Figure 2 shows a cylindrical aluminium bar XY, of mass 5.0 g, resting on two horizontal aluminium rails which are 5.0 cm apart. The rails can be connected to a battery to drive current of 4.5 A through XY. A magnetic field, of flux density 0.15 T, acts into the paper. 

Figure 2

7-8-s-q--q4c-hard-aqa-a-level-physics

Calculate the angle to which the rails must be tilted to keep XY stationary.

4d3 marks

Figure 3 shows a metal rod suspended in a magnetic field by two identical, vertical springs. The cell and rod have negligible resistance. When the switch S is closed, current from the cell flows through the springs and the metal rod. The magnetic field causes the metal rod to be displaced a distance x from its starting point. 

Figure 3

7-8-s-q--q4d-hard-aqa-a-level-physics

Show that when both the spring constant and electrical resistance of each spring is doubled, closing the switch would cause the rod to be displaced a distance begin mathsize 16px style x over 4 end style

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5a2 marks

Two square, parallel metal sheets are separated by 25 mm in a vacuum, the lower plate being earthed. A narrow beam of electrons enters symmetrically between the plates as shown in Figure 1. There is a uniform magnetic field of flux density 0.020 T, which is perpendicular to the beam and parallel to the plates, acting in the direction shown in Figure 1.  When a potential difference of 1500 V is applied to the plates, the electron beam is undeflected.  

Figure 1

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Calculate the speed of the electron, assuming that the electric field between the plates is uniform.

5b5 marks

The potential difference between the plates in Figure 1 can be adjusted. The electrons in the beam are travelling at a speed of 2.35 × 105 m s-1 when they enter just underneath the top plate in the same direction as before.

If the length of the side of each square plate is 5 cm, calculate the maximum potential difference between the plates which would cause the electron beam to just leave the plates at the opposite side to which it entered without touching the lower plate.

Assume that the electric and magnetic fields only act between the plates

5c2 marks

The northern lights are a phenomenon where the sky glows green due to charged particles from the Sun becoming trapped in the Earth’s magnetic fields near the north pole. 

Some charged particles travel in a circle of radius 50 km in a region where the magnetic flux density is 6.0 × 10-3 T.

Show that the charged particles causing the northern lights cannot be electrons.

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1a2 marks

Figure 1 shows a section of a horizontal copper wire carrying a current of 1.3 A.A horizontal uniform magnetic field of flux density B is applied at right angles to the wire in the direction shown in the figure. 

Figure 1

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State the direction of the magnetic force that acts on the moving electrons in the wire as a consequence of the current and explain how you arrive at your answer.

1b2 marks

Copper contains 8.4 × 1028 free electrons per cubic metre. The section of wire in Figure 1 is 125 mm long and has a cross-sectional area of2.8 × 10–5 m2. 

Show that there are about 3 × 1023free electrons in this section of wire.

1c2 marks

With a current of 1.3 A, the average velocity of an electron in the wire is 3.5 × 10–6 m s–1 and the average magnetic force on one electron is 1.8 × 10–25 N.

Calculate the flux density Bof the magnetic field.

1d4 marks

The direction of the magnetic field changes such thatthe weight of the wire is to be

supported by the magnetic force that acts upon it. 

Calculate the minimum value of the flux density of the magnetic field in which the wire should be placed.

   Density of copper = 8.9 × 103 kg m–3

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2a1 mark

The diagram above shows a double-charged positive ion of the iron isotope  F presubscript 26 presuperscript 56 e  that is projected into a vertical magnetic field of flux density 0.18 T, with the field directed upwards. 

Figure 1

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The ion enters the field at a speed of 5.9 × 105 m s–1. 

State the initial direction of the magnetic force that acts on the ion.

2b4 marks

Describe the subsequent path of the ion.Your answer should include both a qualitative description and a calculation. 

Mass of  F presubscript 26 presuperscript 56 e ion = 9.33 × 10–26 kg

2c4 marks

Calculate the time taken for a double-charged iron ionto complete one orbit.

2d4 marks

State the effect on the radius in Figure 1and the time taken to complete an orbit if the following changes are made separately: 

(i)         The strength of the magnetic field is doubled. 

(ii)        A triple-charged positive F presubscript 26 presuperscript 56 e ion replaces the original one.

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3a3 marks

Cyclotrons are used to accelerate particles, such as protons, for a number of applications. 

A cyclotron has two D-shaped regions called ‘dees’ where the magnetic flux density is constant.The dees are separated by a small gap.An alternating electric field between the dees accelerates charged particles. The magnetic field causes the charged particles to follow a circular path. 

Figure 1 shows the path followed by a proton that starts from O.

 Figure 1

screenshot-2023-10-02-094308

State and explain:

(i)

Why it is not possible for the magnetic field to alter the speed of a proton while it is in one of the dees.

(ii)

The direction in which the magnetic field should be applied in order for the protons to travel along the semi-circular paths inside each of the dees.

3b3 marks

Show that the time taken by a proton to travel around one semi-circular path is independent of the radius of the path.

3c2 marks

The maximum radius of the path followed by the proton is 0.46 m and the magnetic flux density of the uniform field is 0.88 T. 

Calculate the maximum speed of a proton when it leaves the cyclotron. 

Ignore any relativistic effects.

3d3 marks

The protons leave the cyclotron when the radius of their path is equal to the outer radius of the dees. 

Ignoring any relativistic effects, calculate the radius required for the cyclotron to produce:

(i)         Protons with a maximum kinetic energy of 25 MeV. 

(ii)        Protons which travel at half the speed of light.

 

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4a2 marks

Discuss two situations in which a charged particle will experience no magnetic force when placed in a magnetic field.

4b3 marks

Figure 1 shows an electron moving through a magnetic field. 

Figure 1

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The magnetic field has a flux density of 0.38 T. The electron travels at a speed of 1.2 × 107 m s–1. 

(i)
Draw the direction of the force acting on the electron due to the magnetic 
(ii)
Calculate the size of the electron’s acceleration.
4c3 marks

An electron is fired into a chamber containing a magnetic field as shown in Figure 2.  The chamber is 60 mm wide and the magnetic field is perpendicular to the plane containing the moving electron. The electron has 6.30 × 10-16 J of kinetic energy. 

Figure 2

7-8-s-q--q4c-medium-aqa-a-level-physics

Calculate the strength of the magnetic field if the electron is to just miss colliding with the opposite plate.

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5a1 mark

A section of a straight current-carrying wire is placed at right angles to a uniform magnetic field of flux density B. When the current in the wire is I, the magnetic force that acts on this section is F. 

A second section of wire is placed at right angles to a uniform magnetic field of flux density 4B when the current is 0.75 I. 

Calculate the force that acts on the second wire.

5b3 marks

The first wire is placed in a uniform magnetic field of flux density B, with current I, and magnetic force F. The uniform magnetic field covers90 mm of the wire. 

The same length of the second wire is placed in a west-east direction as shown in
Figure 1. The magnetic flux density of the second wire is 80 mT and is directed downwards into the plane of the diagram. When a current of 3.0 A passes through the second wire from west to east, a force acts on it.
 

Figure 1

7-8-s-q--q5b-medium-aqa-a-level-physics

Calculate the magnitude and direction of the force on the first wire.

5c4 marks

One of the wires is bent into a square coil. 

The coil is mounted on an axle O and is placed with its plane parallel to the flux lines of a uniform magnetic field B, as shown in Figure 2. 

Figure 2

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Then, the coil is then placed at right angles to the magnetic field as shown in Figure 3. 

Figure 3

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The current, I, is switched on and flows through sides PQRS. 

Before the coil is allowed to move, describe the forces on sides SP and QR in: 

(i)         Figure 2. 

(ii)        Figure 3.

5d2 marks

The wire is then bent into a circular coil, as shown in Figure 4. 

The circular coil is placed in a uniform magnetic field B with the plane of the coil perpendicular to the magnetic field. 

Figure 4

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The current, I, is switched on and flows in a clockwise direction. 

Describe the effect on the coil from the interaction between the current and the magnetic field.

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